JPL announced the stop of the Ulysses mission recently . It is orbiting the sun in a higly inclinated orbit bringing it over the suns poles . In the baut-forum someone analysed the JPL Horizons data and came with the result the spacecraft will have a close encounter with Jupiter in 2098 ...As a result the spacecraft might be ejected out of our solarsystem . ( I don't know if JPL announced this fact itself ). Reason to start a simulation . Animation herunder is generated with frames 6.2 years apart . Visible are Jupiter / Mars and Earth . In 2098 the spacecraft indeed makes a close approach with Jupiter , changing its orbit dramatically , but I wasn't able to get an ejection .

Ulysses got it's special polar orbit 16 years ago by means of a gravity assist to Jupiter . Heres an animation of this gravity asssist . More info can be found on the JPL site . The initial data were obtained from JPL as per 01/02/07 , then the sim was run backwards in time up to the close encounter with Jupiter some 16 years ago . , and the pictures were mounted in resverse order . It's a good point that in this simulation Ulysses seems to come from the direction of Earth . One frame corresponds with 6.2 years.

Partly due to its Earths origin and gravity boost with Jupiter the Ulysses spacecraft is in a near 1:2 resonance with Jupiter . Animated herunder is the spacecrafts orbit in rotating frame to Jupiter ( Jupiter being at 7 'o clock ) . Frames are 6.5 years apart . The craft orbits in a rather unusual pattern until it gets out of its resonance in 2098... Edit : I changed the animation to 12.8 years

Ulysses made a gravity assist to Jupiter in Feb 1992 . Heres an animation showing the Spacecraft approaching Jupiter . Ulysses approaches from the left under , is accelerated , passes behind Jupiter and is swung out in a high inclination orbit . Animation is viewed from Earth . Each dot represents 0.5 hours of time.

Have you tried getting the data just prior to the 2098 ejection and seeing if you can get an ejection that way? Perhaps forces not considered effect the ability to accurately propogate the spacecraft 90 years into the future and still pass Jupiter at the precise distance for an ejection. Spacecraft have very low densities, and may be affected by light pressure.

Well , I don't know if the ejection story is true . I don't find any evidence from the side of JPL . The only thing I can refer to is the ephemeris in 2098 . I think I'll try to find out what JPL has for ephemeris further than 2098. EDIT : the JPL ephemeris for Ulysses stops at 2015 . I wonder where the other guy got his data for 2098

An animation as a side product of the Ulysses animation I think I should share ... Staying on Jupiter and looking towards the sun one can see Mercury performing its orbit around the sun . The wobbling effect is due to the changing point of view . One frame covers 0.5 years.

As a tribute to the spacecraft Ulysses which will be put on rest ... The most beautiful animation I found here : http://www.esa.int/esaSC/SEMAGTUG3HF_index_1.html Simulating the Galilean Moons with GravSim and postprocessing the data in 3D gives the following picture: Viewpoint is the sun . Simulation is run reversed and goes back to the time where Ulysses made its close flyby with Jupiter in order to pump it on a higly inclinated orbit aroud the sun . Timespan is mor than 15 years. In reality Ulysses came from the bottom of the screen , encounters Jupiter and gets in its high inclination orbit .